Rabosh R. Dynamic problems of longitudinal shear for elastic medium with thin-walled elastic inclusion

The thesis deals with the study of the wave fields in elastic media with thin-walled piezoelectric curvilinear inhomogeneities of varying thickness under antiplane dynamic loading.Basing on the approaches of the theory of singular perturbations, the efficient boundary conditions of interaction between a thin curvilinear piezoelectric inclusion and elastic medium for stationary vibrations of composite have been obtained. Different cases of electric boundary conditions on the surface of inclusion at perfect mechanical contact of inhomogeneity and matrix have been considered. The procedure proposed enables as well the investigation of behavior of the stress-strain state of the body in the vicinity of the inclusion edge vs. the shape of this edge. To this end the corresponding internal asymptotic corrections have been constructed.Using the models obtained by means of the Fourier time transform method, BIE method and jump functions method, new problems of elastic wave diffraction by thin piezoelectric inhomogeneities both of small rigidity and weak visibility have been solved.By means of the procedure proposed the dynamic concentration of stresses near the edges (peaked in particular) of thin piezoelectric inclusions has been studied. Principal regularities of the fields scattered by such inhomogeneities into the far zone (Fraunhofer zone) have been shown.